Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedPipeline-generatedverified 2026-09-26 (gpt-6-sol)
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Cellular homology of an infinite-dimensional projective space

Example

Assume the Axiom of Choice. RP∞ has H0≅Z, Hn≅Z/2 for positive odd n, and Hn=0 for positive even n.

Facts & Assumptions

Given: The Axiom of Choice (The Axiom of Choice) and the filtration by finite projective skeleta.

Verification

technique · direct
1.1given

The finite skeleton RPm has the alternating 0,2 cellular complex and the resulting singular homology computed in Cellular homology of real projective space. In each fixed degree these groups and the inclusion maps stabilize once m is larger than that degree.

2.1step 1.1∎

Using the stated Axiom of Choice for the skeletal-colimit theorem, taking the stabilized groups and applying Homology of an infinite CW complex is the colimit of skeletal homology yields the stated infinite-dimensional calculation.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources